I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!

Wednesday, January 02, 2008

Sold Out Flight

On a sold out flight, 100 people line up to board the plane. The first passenger in the line has lost his boarding pass, but was allowed in, regardless. He takes a random seat. Each subsequent passenger takes his or her assigned seat if available, or a random unoccupied seat, otherwise. What is the probability that the last passenger to board the plane finds his seat unoccupied?

When the last passenger boards the plane, there are just two possibilities: the one remaining seat may be his or that of the first passenger Under the assumption that no preference has been exhibited by the boarding passengers towards either of the two seats, they both have the same probability to become the last unoccupied seat: 50%.

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Wednesday, January 02, 2008

Sold Out Flight

On a sold out flight, 100 people line up to board the plane. The first passenger in the line has lost his boarding pass, but was allowed in, regardless. He takes a random seat. Each subsequent passenger takes his or her assigned seat if available, or a random unoccupied seat, otherwise. What is the probability that the last passenger to board the plane finds his seat unoccupied?

When the last passenger boards the plane, there are just two possibilities: the one remaining seat may be his or that of the first passenger Under the assumption that no preference has been exhibited by the boarding passengers towards either of the two seats, they both have the same probability to become the last unoccupied seat: 50%.